If I write the source code of C/C++ in Notepad++, then do I need to attach (plugin) an external compiler to it or not to run it?

Answer 1

i think you have a fundamental missunderstanding here. With notepad++ you would write code, which cannot be not be run at this point. C++ is not interpreted, so you need a compiler like gcc to translate it into machine code, so your OS knows what it is executing.
the plugin itself would just help you making the process of compiling easier (by pressing a button in the UI etc). you will still need to provide a compiler.

Answer 2

To run the code you need to download another program. Visual Studio is one of the best.